How many solutions does the system of equations have?

Question

-2x=-10y+6; x+5y=3

1
2
infinitely many
none

y=4x+3; 2y-8x=3

1
2
infinitely many
none

y-7x=-14; 7y-49x=-2

1
2
infinitely many
none

Answer 1

I meant to type it algebra... whoops!

Answer 2

Here is a quick way to find the slope of a line,
if written in the form Ax + By + C = 0
the slope of the line is -A/B

so for #1
-2x=-10y+6 ---> 2x - 10y + 6 = 0 , slope = -2/-10 = 1/5
x+5y=3 ---- slope = -1/5

so the lines have different slope, so they must intersect in 1 point.

#2
y=4x+3 in the form y = mx + b so the slope is 4

2y-8x=3 ---> 8x - 2y + 3 = 0 , slope is -2/-8 = 1/4
again, different slopes, so 1 solution

do the last one the same way.

Answer 3

So what are the number of solutions?

Answer 4

If they have the same slope they are parallel and never cross unless they also have the same constant and are identical in which case they sit on top of each other and have an infinite number, the same y for very x